turningpoint.test | R Documentation |
Perform a test of statistical independence of a data series by comparing the number of turning points present in the series with the number of turning points expected to be present in an i.i.d. series.
turningpoint.test(x)
x |
a numeric vector or univariate time series. |
If the data is x[1], x[2], ..., x[n], then there is a turning point at the point i if either x[i-1]<x[i] and x[i]>x[i+1], or x[i-1]>x[i] and x[i]<x[i+1]. this function counts the number of turning points in the data, standardises it to have mean 0 and variance 1 and asymptotically tests it against a standard normal distribution. The test statistic is
T = (tp-mu)/sigma, where
tp is the number of turning points present in the series,
mu = 2*(n-2)/3,
sigma = sqrt((16*n-29)/90) and
n is the number of data points in the series.
The test is set up as follows:
H_0
: the data series is i.i.d. (not trending)
H_1
: the data series is not i.i.d. (trending)
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
n |
the number of points in the data series. |
mu |
The expected number of turning points that would be seen in an i.i.d. series. |
sigma |
The standard deviation of the number of turning points that would be seen in an i.i.d. series. |
Missing values are not handled.
Points followed by a point having the exact same value are removed from the data series before computing the test statistic.
This test is useful for detecting cyclic/periodic trends in data series.
Andrew Hart and Servet Martínez
Brockwell, Peter J., Davis, Richard A. (2002) Introduction to Time Series and Forecasting. Springer Texts in Statistics, Springer-Verlag, New York.
Bienaymé, Irénée-Jules (1874). Sur une question de probabilités. Bull. Math. Soc. Fr. 2, 153-154.
diffsign.test
, rank.test
, lb.test
,
markov.test
, diid.test
#Generate an IID standard normal sequence
n <- rnorm(1000)
turningpoint.test(n)
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